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Citation: Corradi, Marco, Borri, Antonio, Righetti, Luca and Speranzini, Emanuela (2017) Uncertainty analysis of FRP reinforced timber beams. Composites Part B Engineering, 113. pp. 174-184. ISSN 1359-8368

Published by: Elsevier

URL: http://dx.doi.org/10.1016/j.compositesb.2017.01.03... <http://dx.doi.org/10.1016/j.compositesb.2017.01.030>

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1

Uncertainty analysis of FRP 1

reinforced timber beams 2

Marco CORRADI 3

Mechanical and Construction Engineering Department, Northumbria University Wynne-4

Jones Building, NE1 8ST, Newcastle upon Tyne, United Kingdom and Department of 5

Engineering, University of Perugia, Via Duranti, 93 06125 Perugia, Italy 6

7

Antonio BORRI 8

Department of Engineering, University of Perugia 9

Via Duranti, 93 06125 Perugia, Italy 10

11

Luca RIGHETTI 12

Mechanical and Construction Engineering Department, Northumbria University Wynne-13

Jones Building, NE1 8ST, Newcastle upon Tyne, United Kingdom 14

15

Emanuela SPERANZINI 16

Department of Engineering, University of Perugia 17

Via Duranti, 93 06125 Perugia, Italy 18

19

KEYWORDS: Composite materials, Timber, Mechanical Testing, Uncertanties. 20

21

ABSTRACT: 22

Timber has been a popular building material for centuries and offers significant sustainable 23

credentials, high mechanical and durability properties. Availability, ease to use, convenience 24

2

and economy have made timber the most used construction material in history but, as it is a 25

natural material, uncertainty in its mechanical characteristics is considerably higher than 26

man-made structural materials. National codes and engineers usually employ high factor of 27

safety to incorporate timber strength uncertainty in design of new structures and 28

reinforcement of existing ones. This paper presents the results of 221 bending tests carried 29

out on unreinforced and reinforced soft- and hardwood beams (fir and oakwood) and 30

illustrates the reinforcement effect on timber capacity and strength uncertainty. 31

Both firwood and oakwood beams have been tested in flexure before and after the application 32

of a composite reinforcement made of FRP (Fiber Reinforced Polymer) unidirectional sheet. 33

The uncertainty in the strength of reinforced timber is also quantified and modelled. Test 34

results show that the FRP reinforcement is effective for both enhancing the beam load-35

carrying capacity and for reducing strength uncertainties. 36

37

INTRODUCTION 38

The use of timber in construction is continuously increasing in Europe: information suggests 39

that UK sawn softwood use is about 0.14 m3 per capita compared to 0.20 m

3 in Germany and 40

0.80 m3 in Finland [1]. Timber offers significant sustainable credentials and good mechanical 41

properties. The use of timber structural elements is also an interesting earthquake resistant 42

solution compared to other traditional construction materials like concrete and masonry, 43

based on its lightness, large deformation capacity and high tensile strength and strength-to-44

weight ratio. As a renewable and sustainable material, governments and international 45

regulatory bodies are committed to increase the use of timber and of new wood-based 46

products in construction, by incentivizing it by means of income-tax deduction, valuable 47

funding. 48

3

Because wood has been used as a building material for hundreds of years [2], the upgrading 49

of pre-existing timber structures is another important aspect: increasing the strength of timber 50

beams when their size is incorrect over the span they need to cover or due to an increases in 51

bending loads is often necessary in historic constructions in many parts of the planet [3]. A 52

very large number of historic construction across Europe, representing a significant 53

percentage of the building stock, needs to be not only preserved and protected but also 54

maintained according to the original intended use. Conservation bodies often deal with 55

finding new uses for redundant historic constructions without affecting their significance. 56

As a natural material, the strength of timber is appreciably reduced by the presence of defects 57

like knots, especially when located on the tension side, and distortion of the grain. For this 58

reason uncertainty in the strength of timber is considerably higher compared to an artificial 59

construction material (steel, concrete, bricks, etc.), which is produced through quality-60

controlled and precise manufacturing methods and processes. This uncertainty necessitates 61

the adoption of a conservative approach in evaluating the strength of the material when 62

designing timber beams. This aspect has not been sufficiently investigated in the past and, 63

when an existing timber structure or component does not comply with new standards, 64

structural engineers often opt for removal and demolition or apply strategies based upon 65

reinforcement methods. 66

Remedial methods for upgrading and conservation of old timber beams include the 67

reconstruction of deteriorated parts, the application of metal reinforcements [4-6] and, more 68

recently, mechanical retrofitting techniques employing FRPs (Fiber Reinforced Polymers) 69

and thermosetting resins. For example, Borri et al. [7] tested beams reinforced with carbon 70

sheets (CFRP) applied on the tension side. The tests proved that the application of the carbon-71

fiber reinforcement was mainly beneficial in terms of bending capacity. Similar tests on small 72

beams have been carried out by Plevris and Triantafillou [8], Fiorelli and Dias [9], Radford et 73

4

al. [10] and Hay et al. [11] using fiberglass sheets. The use of carbon pultruded plates has 74

been studied by Raftery et al. [12-13], Nowak et al. [14-16], D’Ambrisi at al. [17], Schober 75

·and Rautenstrauch [18]. Shear or local reinforcements using FRP sheets have been studied 76

by Triantafillou [19] and Schober et al. [20]. Glued laminated timber (glulam), made of 77

multiple layers of dimensioned lumber bonded together with durable, moisture-resistant 78

structural adhesives, has been also reinforced with FRPs (sheets, plates or bars) and high 79

increases in bending capacity have been measured [21-25]. 80

The use of composite rods or bars inserted in grooves at the tension side of timber beams has 81

also been suggested as a means of reinforcing and repairing existing timber beams (Svecova 82

and Eden [26], Micelli et. al. [27], Alam et al. [28]). Gentile et al. [29] tested twenty-two half 83

scale and four full-scale timber beams strengthened using GFRP bars to failure and found a 84

flexural strength increase up to 46%. Righetti et al. [30] studied the shear stress distribution 85

along a groove-embedded CFRP bar. 86

Composite sheets made of natural fibers (bamboo, flax, hemp, basalt) have been studied by 87

Borri et al. [31] and de la Rosa García et al. [32]. More recently composite sheets made of 88

high strength steel cords embedded into an epoxy putty have been used to reinforce timber 89

beams [33]. 90

Among retrofitting methods using composite materials, the subject of FRP reinforcement 91

using pre-impregnated sheets generated considerable interest within the research community 92

mainly because this method proved to be the most effective in terms of strength 93

improvement. Ease of application, limited damage to the timber substrate in case of removal, 94

low-cost and fast reinforcement procedures are the key features of the use of epoxy-bonded 95

FRP sheets. 96

This paper presents the results of an experimental investigation of the behaviour of 221 97

unreinforced and reinforced timber beams. Reinforcement has been applied using FRP pre-98

5

impregnated unidirectional sheets placed on the tension side of a very large number of timber 99

beams using an epoxy gluing system. Specimens were made of common commercially-100

available softwood (Firwood - Abies Alba) and hardwood (Oakwood – Quercus Petraea) 101

beams. Enhancement of the behavior of timber beams in bending by the addition of a 102

composite reinforcement is not a new concept, but the analysis of the strength uncertainty of 103

both commercially available unreinforced and FRP-reinforced timber beams has not been 104

addressed before. A first attempt to address this problem is reported in [34]. Uncertainty 105

analysis was only studied with regard to the short term static performance. No analysis was 106

undertaken with regard to fatigue, long term and dynamic performance. The presence of FRP 107

sheets seems to delay crack opening on the tension side, confines local rupture and bridges 108

local defects in the timber and this has a considerable effect on the strength properties. 109

110

UNREINFORCED TIMBER 111

The bending strength of timber is governed by the modes of failure. Since the behavior of 112

timber in compression is different from that in tension, the failure modes could be highly 113

affected by this. Figure 1 show different characteristic failures of beams in bending. Simple 114

tension failure (Fig. 1a) due to a tensile stress parallel to the grain. This is common in 115

straight-grained beams made of high quality timber, particularly when the wood is well 116

seasoned and there is no diagonal cross grain. 117

The most common failure mode is the cross-grained tension, in which the fracture is caused 118

by a tensile force acting oblique to the grain. This is a common form of failure especially 119

where the beam has diagonal or other form of cross grain on its tension side. This failure 120

mode, always occurring on the beam tension side, can be also activated by the presence of 121

defect (a knot, a shake, etc.). Example of such failures are shown in Figure 2. Since the 122

6

tensile strength of wood across the grain is only a small fraction of that with the grain it is 123

easy to see why a cross-grained timber would fail in this manner. 124

As stated, an interesting effect of the analysis of the failure modes is that these usually occurs 125

for different levels of bending loads. Failure mode in Figure 1b is usually activated for low 126

bending loads. This is also typical of low-grade timber where the high number of defects 127

facilitates the cross-grained tension failure. 128

Failure on compression side is shown in Fig. 1c. This failure mode do not usually lead to the 129

collapse of the structure as the behavior of timber in compression is plastic (Fig. 3). Failure 130

modes in Figure 1a is usually activated for high bending loads as this occurs for straight-131

grained beams and tensile strength of timber is very high. 132

While generally tensile fracture governs bending capacity, other mode of failure is horizontal 133

shear rupture, in which two portions of a timber beam slide along each other. This failure 134

mode is rare for large timber beams, but it can occur in the case of large beams with openings 135

and often require local reinforcement [35]. It is often due to shake checks, which reduce the 136

resisting cross sectional area. The consequence of a failure in horizontal shear is to divide the 137

beam into two or more parts the combined capacity of which is much less than that of the 138

original beam. Figure 1d shows a large beam in which a horizontal shear failure occurred at 139

one end. 140

The application of an external FRP reinforcement causes an increase in the bending capacity 141

for different reasons. Firstly because high-strength composite material is added on the tension 142

side increasing the resisting cross sectional area, but also because this could prevent the 143

occurrence of a failure mode characterized by a low capacity. This is the case of a FRP-144

reinforcement epoxy-glued on the tension side: the initiation of the fracture mechanism 145

produced by the grain deviation or the presence of a knot on the beam’s tension side is 146

7

postponed or stopped (Fig. 4) and the beam will fail according to a different failure mode 147

with a higher bending capacity. 148

149

Strength grading 150

The main mechanical properties of timber are usually estimated using a process known as 151

strength grading. This is usually conducted at the sawmills when the timber elements are 152

produced. Grading is usually carried out by visual assessment or by machine by the 153

companies selling the timber material for structural applications. Visual strength grading is 154

made using the grader’s experience across a number of factors (dimensions and density of 155

knots, grain deviation, annual rings characteristics, etc.) while machine strength grading is 156

best suited to high volumes of wood where the species and the dimension of the cross section 157

are not changed very often. 158

The European standard for timber [36-37] includes several strength classes. These classes are 159

designed by a letter (D for deciduous species and C for coniferous and poplar) followed by a 160

number. The number represents the characteristic lower 5th

percentile value of the bending 161

strength of 150 mm deep timber in MPa. Strength grading of timber beams is often done by 162

machine to Standard EN14081 [38] to twelve classes ranging between C14 and C50 and to 5 163

strength classes (D30, D40, D50, D60 and D70) for softwood and hardwood, respectively. 164

It is recognized that some sawmills in Slovenia did not perform grading properly prior to the 165

introduction of harmonised standards [39]. In many cases in small production sites in Europe 166

no grading is applied or a fee is charged for this service [40-41]. In order to comply with 167

European Standards, to avoid risks associated with unmet strength requirements and to 168

economize on the grading process (sometimes more expensive for high quality timber), a lot 169

of companies prefer to grade their timber production with low strength values, especially if 170

they produce low-added value products, like timber beams for the construction industry. It is 171

8

also common that the sawmills ask the client for an additional cost for the grading service: 172

this often costs a fee or an additional 20% for of the price of D40 timber (and higher strength 173

classes) and 10% for D30. 174

In some cases, when this is possible, both final users and producers opt not to use graded 175

timber. Producers of engineered wood products can use material that has not been pregraded 176

if they undertake the mechanical properties characterisation themselves. When grading is 177

needed, a lot of sawmills grade their beams in the C16 class (for firwood beams), even if the 178

strength quality of their products is higher, especially because the stiffness is often the 179

controlling factor. For oakwood beams (hardwood), the typical strength class of the products 180

on the market is D30. 181

The main consequence of this incorrect application of the European standard is that a very 182

limited choice of timber is available on the market for the higher strength classes and, for the 183

lower strength classes (C16, D30, etc), the mechanical characteristics are very scattered as 184

this is simply used as a lower strength bound. 185

186

Experimental work 187

In this experimental work, a large number of oak and firwood beams were used and tested in 188

bending before and after the application of an FRP reinforcement. For both wood species 189

different beam dimensions were tested with cross sections varying from 20x20 mm to 190

200x200 mm. D30 and C16 strength classes were used for oak and firwood beams, 191

respectively. 192

Mechanical properties of both wood species were partially evaluated in accordance with 193

ASTM D143 [42]. A parallel to the grain compressive strength of 27.9 MPa (Coefficient of 194

Variation (CoV) = 9.6%) and 31.7 MPa (CoV = 7.9%) was measured from firwood and 195

hardwood prismatic test specimens (20x20x60 mm), respectively. The average weight 196

9

densities were 791.8 and 423.7 kg/m3 for firwood and hardwood. Moisture contents were 197

12.5 and 11.9 % and were measured according to EN 13183-1 standard [43]. 198

199

Unreinforced beams 200

Six series of bending tests were performed on unreinforced softwood (fir) and hardwood 201

(oak) beams (Tab. 1). In total 95 unreinforced beams were subjected to four-point-bending 202

test (Fig. 5), according to UNI EN 408 [44] standard for flexural strength estimation. The 203

beams were new and with straight and sharp edges. All beams were found on the market and 204

had a square cross section. The dimensions of the three series of softwood beams were 205

20x20x380 mm, 100x100x1950 mm and 200x200x4000 mm. For hardwood beams, 206

dimensions were 20x20x380 mm, 67x67x1320 mm and 200x200x4000 mm. 207

In order to reduce the local crushing of the wood, the load was applied through two diameter 208

steel cylinders. Displacement controlled loading ensued with a crosshead speed of 2-4 209

mm/min. The load was applied monotonically until failure by means of a hydraulic jack 210

connected by a hydraulic circuit to a pump. The vertical displacements of the beams were 211

recorded using inductive transducers (LVDT) in the testing region (pure bending region) to 212

monitor the mid-span deflection and calculate the curvature. 213

Hardwood is usually characterized by higher mechanical properties compared to softwood. 214

However uncertainties are usually more significant compared to softwood like fir, larch and 215

pine woods. Grain deviation and dimensions of the knots are larger, but the density of the 216

knots are usually smaller. For this reason it was decided to test one common type of 217

hardwood (oak) and one of softwood (fir). The test program was divided into two series: tests 218

on beams unreinforced and reinforced with FRP sheets. Tests results were then processed 219

according to the indications of the reference standards and the bending strength fm evaluated 220

thus: 221

10

W

Faf u

m2

(1) 222

where, Fu is the ultimate (maximum) load (N), a is the distance between the point of 223

application of the load and the nearest support (mm) and W is the modulus of resistance of 224

the section (mm3) about the neutral axis. 225

Results for unreinforced beams are given in Table 1. In this table results are reported in terms 226

of mean bending strength value (fm) and its standard deviation. fm,k is the strength value at 5% 227

of cumulative distribution function. 228

The relationship between bending load and mid-span displacement (Fig. 6) was initially 229

linear. As the load increased, timber started to yield on the compression side and tensile 230

failure occurred when the tensile strength was reached. In most cases, failure initiated by 231

flows in the timber material (knots, grain deviation, splits or cracks). Table 1 shows that the 232

scattering in the capacity values of un-reinforced large beams (200x200 mm and 100x100 233

mm cross sections), where the presence of grain deviation and knots have an influence on the 234

failure mode, is very high. The Coefficient of Variation (CoV), also known as Relative 235

Standard Deviation, of the bending strength was 28.26 and 34.72 % for 200x200 mm cross 236

section (oakwood) and 100x100 cross section (firwood) beams, respectively. It is worth 237

noting that for the 95 unreinforced timber beams tested in bending, the CoV was smaller for 238

small beams. Even if the number of tested beams was not very high, this result can be 239

considered interesting. The explanation of this is apparent from the analysis of the 240

dimensions of defects, mainly knots, compared to the dimensions of the timber beams: 241

typical knot defects have a diameter varying from 3 to 10 cm and, for small beams, this may 242

lead to early catastrophic failures when loaded, as the knot may completely interrupt the 243

continuity of timber fibers. For this reason sawmills are forced to check small beams by 244

discarding the defected ones or by cutting off the parts where the defects are located before 245

commercialization. This has a positive effect on both the strength and its scattering. 246

11

When the dimensions of the beams are bigger, the effect of a single defect is limited. In this 247

situation sawmills may pay less attention to the defects. However large beams, when tested in 248

bending, exhibit a large scattering in the bending strength. 249

Table 1 and Figures 7-8 show the Probability Density Function (PDF) and Cumulative 250

Distribution Function (CDF) of the strength for unreinforced beams. It can be noted that the 251

fm,k value was largely below 16 MPa (value given as a limit by the EN 338 standard [36] for a 252

C16 wood) for 100x100 mm firwood beams. The difference was even bigger for 200x200 253

mm oakwood beams. By comparing the experimental result of fm,k (17.92 MPa) and the value 254

given by the EN 338 standard (30 MPa for D30 wood) it can be noted a difference of approx. 255

35 %. These low values of fm,k were clearly the consequence of the high scattering of the test 256

results: in fact, the mean experimental value of the bending strength fm was always greater 257

than the value given by the EN 338 standard. 258

It is not possible to verify how common is the fact that there are on the market timber beams 259

that are not meeting the requirements of the EN 338 standard in terms of bending strength. 260

However the tests carried out in this experimental research seem to indicate that this is not 261

very rare, especially for beams of large dimensions. 262

263

REINFORCED TIMBER 264

126 timber beams were reinforced using Carbon (CFRP) or Glass (GFRP) sheets. Both 265

composite sheets had similar weight densities (0.3 and 0.288 kg/m2 for carbon and glass 266

sheet, respectively). The current market price is approx. 7.2 and 14 €/m2 for carbon and glass 267

sheet. The popularity of bonded FRP reinforcement of timber is largely due to the economy 268

with which they may be applied with low installation times than other strengthening methods. 269

Reinforcement can be easily made on-site (hand lay-up technique) by applying the matrix 270

polymer (usually an epoxy resin) over the fibers (Fig. 9). The same resin is often used as 271

12

matrix polymer to form the FRP composite and as bonding adhesive with the wooden 272

substrate. 273

The component materials of the FRP-strengthened beams were characterized before beams 274

were examined under load. Mechanical properties of glass and carbon fibers, according to the 275

procedure outlined in the ASTM Standard D3039 [45], are shown in Table 2. 276

Reinforcement and resin were applied by hand lay-up (Fig. 9a, 9b). Once the composite layer 277

was placed over the beams (Fig. 9c), resin was applied either by pouring on by hand. The 278

layer was consolidated and air bubbles were removed by using squeegees and hand rollers. 279

Beams were tested in bending according to the same test arrangement used for unreinforced 280

beams (Fig. 5). The failure mode was not highly influenced by the type of reinforcement 281

(Carbon or Glass fibers), as the failure usually occurred in the wood material, without 282

attaining the ultimate FRP tensile strength (Fig. 10). On the contrary, the cross sectional area 283

and the area fraction of the composite material had a significant influence (Tab. 3). 284

When FRP reinforcement failure is neglected due to its high tensile strength, two different 285

failure mechanisms are possible. The first one involves the possibility of attaining the wood 286

tensile strength, while the other occurs when the compressive stress limit is reached. The two 287

stress limits were often attained consecutively: experimental tests have shown that the most 288

frequent failure mechanism was the one in which tensile failure occurred, but this was 289

preceded by a partial plasticization of timber material at the compression side, both for un-290

reinforced and reinforced beams (Fig. 10). 291

The application of the composite reinforcement resulted in a downward movement of the 292

neutral axis position and an increase in the beam capacity, as shown in Figure 10. The 293

increment in the bending stiffness was usually very limited [7, 9, 20, 31]. However, some 294

studies reported significant increases in stiffness especially for CFRP reinforcement of lower 295

grade timber or high reinforcement ratios [8, 10, 12]. Analyzing the distribution of forces 296

13

over the entire section, it was possible to state that the reinforcement, applied on the tension 297

side, was very useful in improving the ultimate resisting moment, through the contribution of 298

an extra tensile force (F3). 299

Furthermore, this reinforcement allowed a greater axial deformation in the compression 300

region, as a result of the increase in the distance of the compressed wood fibers from the 301

neutral axis. This type of intervention may be used for low grade timber due to the presence 302

of defects, such as timber in which the ratio between ultimate tensile and compressive 303

stresses is approx. 1. When timber yielded on the compression side, the values of forces F1, 304

F2 and F3 were very high. However the point of application of force F1 moved downward 305

causing a decrease of the offset of internal forces. Force F3, generated by the FRP 306

reinforcement, allowed an increase in the resisting moment. 307

The application of the composite reinforcement had several positive effects: 1) It caused a 308

significant increase in the beam’s bending capacity; 2) The reinforced beams exhibited a 309

more ductile behavior, as an higher degree of yielding was possible on the beam’s side in 310

compression; 3) According to the results shown in Table 4, the FRP reinforcement also 311

reduced the standard deviation in the strength value. Figures 11 and 12 show the PDF and 312

CDF functions for reinforced beams. Several experimental tests [3] have shown that the most 313

frequent failure is a tensile failure without the timber plasticization of the compression 314

region, depending on the quality of the wood. This explains the need for a composite 315

reinforcement on the tension side, especially for low-grade timber. 316

Figure 13 shows a comparison between the increments of reinforced firwood beams in terms 317

of mean bending capacity and fm,k values. The increment, calculated using the fm,k values, is 318

always bigger compared to the one based on the mean bending strengths fm. The maximum 319

ratio between the two increments (fm,k increment / mean capacity fm increment) was 3.24, and 320

this occurred for 100x100 mm cross section beams reinforced with GFRPs. This increment 321

14

was usually greater for beams of large dimensions (it was approx. 1 for beams having 20x20 322

mm cross sections) based on the fact that larger beams contains defects of various, such as 323

knots, slope of grain, bark pockets, etc. In this situations the application of a FRP 324

reinforcement may produce a double positive effect as it confines local ruptures and bridges 325

local defects in the timber. 326

It can be also noted that both unreinforced and reinforced timber beams were tested over a 327

short span. This reduced the probability of the presence of a critical defect in timber, 328

decreasing the uncertainty of timber beams, particularly when unreinforced. It is likely that 329

with longer spans uncertainty of unreinforced beams will increase and the positive effect of 330

the composite reinforcement should be even more noticeable. Also, it should be noted that no 331

measures to minimize the difference in properties between the timber beams in each group or 332

adjustment factors to the stiffness and strength values have been applied for the data reported 333

in Tables 4 and 5. 334

By comparing these results with the ones reported in [46] for timber beams reinforced with 335

unbonded composite plates, it can be noted that the increments in the bending capacity were 336

significantly larger when the FRP reinforcement was bonded to the beam’s tension side with 337

an epoxy adhesive. The role of the resin seems to be critical in both the stress transfer (FRP-338

timber) and in confining local ruptures in the timber. This had a considerable effect in 339

reducing the uncertainties and in increasing the fm,k value of reinforced beams. 340

On the contrary, the difference in terms of capacity increments between GFRP- and CFRP 341

reinforced beams was smaller. For high reinforcement area fractions (Fig. 13) the ratio 342

between these increments decreased. By comparing the test results of GFRP- and CFRP-343

reinforced beams for the same cross section (Tab. 5), it can be noted a limited difference in 344

terms of capacity increments for beams reinforced with the two FRP types. CFRP had a 345

much higher tensile strength (3388 MPa, Tab. 2) compared to GFRP (1568 MPa) but this did 346

15

not cause a significant increase in the beam bending capacity. Because failure always 347

occurred on the beam’s tension side, the composite tensile strength could not be completely 348

exploited during the tests and this reduced the importance of using a carbon sheet, more 349

expensive and with higher mechanical properties. 350

With regard to the flexural stiffness r, the application of a FRP reinforcement did cause a 351

significant increase in the mean value of this mechanical property. Flexural stiffness was 352

calculated from the bending load F – midspan deflection ( graph by considering the slope 353

of the secant line between F1 =0.1x Fmax and F2 =0.5 x Fmax: 354

12

12

FF

FFr

(2) 355

where 2F and

1F are the corresponding values of the midspan deflection. 356

For both unreinforced and reinforced beams, the CoV of the flexural stiffness r was always 357

smaller compared to the CoV of the strength. Defects in timber affect more the strength than 358

the stiffness, causing a smaller scattering of the r values. 359

FRP reinforcement also produced a limited increase of the flexural stiffness (r increment = 360

approx. 5-15%) based on the fact that the reinforcement area fractions (Tab. 3) were very 361

small. Furthermore, the orientation of the FRP sheet (parallel to the neutral axis of the beam’s 362

section) (Fig. 10) produced a very small increase in the cross section’s total second moment. 363

By comparing the increments of r and Kr values (flexural stiffness at 5% of cumulative 364

distribution function), it can be noted that these increments were similar (Tab. 5) highlighting 365

the fact that the application of the reinforcement was not able to reduce stiffness uncertainty. 366

367

CONCLUSIONS 368

Epoxy-bonded FRP sheets appear to have good potential to strengthen existing deficient 369

timber beams. In this experimental investigation 221 fir and oakwood beams were tested and 370

16

it was demonstrated that the application of small quantities of composite reinforcement, 371

besides being an effective method of increasing timber beam’s capacity, also reduced the 372

uncertainties in the strength. 373

Tests results showed that the typical failure modes for unreinforced and reinforced beams 374

were gross-grained tension and knot initiated. Ductile compression did not produce the beam 375

failure and the rupture always occurred on the tension side. The application of an epoxy-376

bonded FRP sheet confined local rupture and bridged local defects in the timber and this had 377

a considerable effect on the beam capacity and on the scattering of the results. The negative 378

defects effect on the tension side was effectively reduced by the application of the FRP 379

reinfocercent. Increments in the mean strength up to 122% and decrements in the CoV values 380

up to 62.5% were experimentally found. All tested timber beams (made of firwood and 381

oakwood) met, after reinforcement, the requirement of the EN 338 standard for the strength 382

class for which they were commercialized and sold. 383

Finally it is worth noting that a limited difference in terms of capacity increments was 384

recorded for beams reinforced with the two FRP types (GFRP and GFRP). Because failure 385

always occurred on the timber beam’s tension side, the FRP tensile strength could not be 386

completely exploited during the tests and this reduced the importance of using a composite 387

material with higher mechanical properties (CFRP). 388

389

REFERENCES 390

[1] FAO, Food and Agriculture Organization of the United Nations. State of the World’s 391

Forests. 2011. 392

[2] Thelandersson S, Larsen HJ. Timber engineering. John Wiley & Sons. 2003. 393

[3] FHWA, US Department of Transportation. Seventh annual report to the congress on 394

highway bridge replacement and rehabilitation program. 1986. 395

17

[4] Lantos G. The flexural behavior of steel reinforced laminated timber beams. Wood 396

Science 1970; 2: 136-43. 397

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486

ACKNOWLEDGEMENTS 487

The authors wishes to record their indebtedness to Mr A. Molinari, A. Ricci and A. Maraca 488

for their contribution to part of the experimental work. Thanks are also due to the Civil 489

Engineering Laboratory Staff of the University of Perugia, Italy. 490

491

21

LIST OF FIGURES 492

Figure 1: Characteristic failure modes of simple beams: a) tension failure for straight-grained 493

beams b) the cross-grained tension failure c) compression failure, d) horizontal shear rupture. 494

Figure 2: Tension failure modes: a) due to the presence of a knot on tension side, b) simple 495

tension (tension failure for a straight-grained beam), c) and d) cross-grained tension failure. 496

Figure 3: Typical stress distribution for a tension failure. 497

Figure 4: Typical cross grained tension failure and subsequent FRP debonding. 498

Figure 5: Test arrangement (four-point bending) and LVDT position (1/4 and 3/4 of the span, 499

mid-point). 500

Figure 6: Load vs mid-span deflection for softwood beams having a 100x100 mm cross 501

section: the relationship is initially linear and, for beams of good quality at high load level, 502

the curves flatten as a consequence of timber yielding on the compression side. 503

Figure 7: Probability Density Function (PDF) for unreinforced beams (different cross 504

sections): a) firwood b) oakwood. 505

Figure 8: Cumulative probability: a) 100x100 mm firwood beams, b) 200x200 oakwood 506

beams. 507

Figure 9: Reinforcement procedure: a) application of a first layer of epoxy resin, 2) fibers can 508

be easily cut with scissors, 3) multiple sheets of fibers can be also applied and alternated with 509

multi-layers of epoxy coatings. 510

Figure 10: Stress and strain distribution, before and after timber yielding in compression. 511

Figure 11: Unreinforced and reinforced firwood beams (100x100 mm cross section): a) PDF 512

b) CDF. 513

Figure 12: GFRP vs. Unreinforced for 100x100 mm and 200x200 mm cross sections. 514

Figure 13: Comparison between increments of reinforced firwood beams in terms of fm 515

(mean bending capacity) and fm,k values. 516

22

LIST OF TABLES 517

Table 1: Test results for unreinforced wood beams. 518

Table 2: Results of mechanical characterization of FRP-materials. 519

Table 3: Reinforcement of FRP-materials. 520

Table 4: Test results for reinforced wood beams. 521

Table 5: Effects of reinforcement. 522

23

523

524

Figure 1: Characteristic failure modes of simple beams: a) tension failure for straight-grained 525

beams b) the cross-grained tension failure c) compression failure, d) horizontal shear rupture. 526

527

a) b) 528

c) d) 529

Figure 2: Tension failure modes: a) due to the presence of a knot on tension side, b) simple 530

tension (tension failure for a straight-grained beam), c) and d) cross-grained tension failure. 531

532

a)

b)

c)

d)

24

533

534

535

Figure 3: Typical stress distribution for a tension failure. 536

537

538

Figure 4: Typical cross grained tension failure and subsequent FRP debonding. 539

540

Figure 5: Test arrangement (four-point bending) and LVDT position 541

(1/4 and 3/4 of the span, mid-point). 542

543

FRPComposite

debonding

Cross

Section

Lateral

View

Bending

moment

FRP

epoxy-bonded Cross-grained

tension failure

Spa

n

13 S

pan

LVDT

12 F

12 F

Bending moment

Side in compression

Side in tension

Neutral axis

Compressive stress

Tensile stress

Timber beam

25

544

545

Figure 6: Load vs mid-span deflection for softwood beams having a 100x100 mm cross 546

section: the relationship is initially linear and, for beams of good quality at high load level, 547

the curves flatten as a consequence of timber yielding on the compression side. 548

549

550

551

a) b) 552

Figure 7: Probability Density Function (PDF) for unreinforced beams (different cross 553

sections): a) firwood b) oakwood. 554

555

26

556

Figure 8: Cumulative probability: a) 100x100 mm firwood beams, b) 200x200 oakwood 557

beams. 558

559

560

a) b) 561

c) 562

Figure 9: Reinforcement procedure: a) application of a first layer of epoxy resin, 2) fibers can 563

be easily cut with scissors, 3) multiple sheets of fibers can be also applied and alternated with 564

multi-layers of epoxy coatings. 565

566

27

567

568

Figure 10: Stress and strain distribution, before and after timber yielding in compression. 569

570

571

572

573

a) b) 574

Figure 11: Unreinforced and reinforced firwood beams (100x100 mm cross section): 575

a) PDF b) CDF. 576

577

h

h ˜ h

y

Wtmax

2

Wc

Wtmax

2

PP

Wt

WcmaxWcmax

WtmaxP

Wcmax

Wtmax

P

Wcmax

1

Normal strain Normal stress

Neutral axis

F

2F

3F

Before yielding

After yielding in compression

t

28

578

Figure 12: GFRP vs. Unreinforced for 100x100 mm and 200x200 mm cross sections. 579

580

581

582

Figure 13: Comparison between increments of reinforced firwood beams in terms of fm 583

(mean bending capacity) and fm,k values. 584

585

586

29

587

Table 1: Test results for unreinforced wood beams. 588

Wood

species

Cross

section

(mm)

Sample

size

Weight

density

(kg/m3)

Moisture

content

(%)

Bending

Strength

(MPa)

CoV

(%)

Standard

deviation

(MPa)

fm,k

(MPa)

Fir 20x20 20 423.3 10.2 42.39 14.42 6.10 32.3

Fir 100x100 20 417.0 14.3 23.73 34.72 8.24 10.1

Fir 200x200 10 430.8 11.3 30.32 20.21 6.13 20.4

Oak 20x20 20 823.5 11.6 71.53 13.46 9.58 46.2

Oak 67x67 20 755.8 14.4 60.94 16.90 10.3 44.1

Oak 200x200 5 796.0 11.5 33.83 28.26 9.6 17.9

589

590

591

592

Table 2: Results of mechanical characterization of FRP-materials. 593

Composite type CFRP GFRP

Layout Textile Textile

No. of samples tested 10 10

Fiber orientation Unidirectional Unidirectional

Young’s modulus (GPa) 417.6** 78.65**

Weight density (kg/m2) 0.3 0.288

Tensile strength (MPa) 3388** 1568**

Thickness (mm) 0.165* 0.118*

Elongation at failure (%) 1.0 2.1

* nominal ply thickness ** using nominal thickness for calculation 594

595

596

30

597

598

Table 3: Reinforcement of FRP-materials. 599

Beam cross section (mm) 20x20 67x67 100x100 200x200

No. of beams tested 50 35 24 17

No. of composite layers 1 1 1 2

GFRP area fraction (%) 0.590 0.176 0.118 0.059

CFRP area fraction (%) 0.825 0.246 0.165 0.082

Sheet width (mm) 20 67 100 100

600

601

602

Table 4: Test results for reinforced wood beams. 603

Wood

species

Cross

section

(mm)

Sample

size

Weight

density

(kg/m3)

Moisture

content

(%)

Bending

Strength

(MPa)

Reinforcement

CoV

(%)

Standard

deviation

(MPa)

fm,k (MPa)

Fir 20x20 20 423.3 10.2 70.1 GFRP 13.1 9.11 55.1

Fir 20x20 20 423.3 10.2 94.0 CFRP 16.0 15.0 69.2

Fir 100x100 14 417.0 14.3 32.8 GFRP 18.7 6.11 22.7

Fir 100x100 10 417.0 14.3 39.3 CFRP 20.6 8.12 25.9

Fir 200x200 6 430.8 11.3 45.8 GFRP 10.7 4.91 37.7

Fir 200x200 6 430.8 11.3 48.2 CFRP 8.84 4.32 41.1

Oak 20x20 10 823.5 11.6 130.1 CFRP 7.35 9.60 114.3

Oak 67x67 20 755.8 14.4 89.60 GFRP 18.6 16.7 62.0

Oak 67x67 15 755.8 14.4 83.10 CFRP 9.44 8.80 68.6

Oak 200x200 5 796.0 11.5 48.55 CFRP 10.6 5.14 40.1

604

605

606

31

607

608

609

610

Table 5: Effects of reinforcement. 611

Cross

section

(mm)

Wood

species

Reinforcement

Mean

strength

fm

increment

(%)

CoV

decrement

(%)

fm,k

increment

(%)

Stiffness

r

increment

(%)

Kr

increment

(%)

20x20 Oak GFRP 81.9 45.4 147 11.6 12.2

20x20 Fir GFRP 65.4 9.20 70.6 13.3 13.1

20x20 Fir CFRP 122 -11.0 114 15.1 17.9

67x67 Oak GFRP 47.0 -10.1 40.6 7.8 9.8

67x67 Oak CFRP 36.4 44.1 55.6 9.4 8.1

100x100 Fir GFRP 38.2 46.1 125 9.1 12.0

100x100 Fir CFRP 65.6 40.7 156 11.2 14.0

200x200 Oak CFRP 43.5 62.5 124 4.7 5.0

200x200 Fir GFRP 51.1 47.1 84.8 7.9 7.9

200x200 Fir CFRP 59.0 56.3 101 11.9 8.4

612

613

614